{"id":2855,"date":"2023-12-06T19:05:53","date_gmt":"2023-12-06T18:05:53","guid":{"rendered":"https:\/\/math.univ-lyon1.fr\/dream\/?p=2855"},"modified":"2025-12-05T13:30:52","modified_gmt":"2025-12-05T12:30:52","slug":"les-triangles-rectangles-entiers","status":"publish","type":"post","link":"https:\/\/math.univ-lyon1.fr\/dream\/?p=2855","title":{"rendered":"Les triangles rectangles entiers"},"content":{"rendered":"\n<h2>\n\t\t\t\u00c9nonc\u00e9 du probl\u00e8me\t<\/h2>\n\t<p><strong>Version g\u00e9om\u00e9trique<\/strong> : Quels sont les triangles rectangles dont la longueur de chaque c\u00f4t\u00e9 est un nombre entier naturel ?<\/p>\n<p><strong>Version arithm\u00e9tique<\/strong> : D\u00e9terminer l&rsquo;ensemble de triplets pythagoriciens , c&rsquo;est-\u00e0-dire les triplets d&rsquo;entier (x,y,z) \u2208 N\u00b3 tels que x\u00b2 + y\u00b2 = z\u00b2<\/p>\n\t\t\t<a href=\"https:\/\/math.univ-lyon1.fr\/dream\/?page_id=79\" target=\"_self\">\n\t\t\t\t\t\tRetour Panier \u00e0 probl\u00e8mes\n\t\t\t\t\t<\/a>\n\t<h3>Connaissances math\u00e9matiques<\/h3>\n\u2666 Le th\u00e9or\u00e8me de Pythagore (comme caract\u00e9risation d&rsquo;un triangle rectangle ou pour calculer une longueur manquante dans un triangle rectangle)<br \/>\n\u2666 Conservation des angles et proportionnalit\u00e9 des longueurs dans un agrandissement\/r\u00e9duction, triangles semblables<br \/>\n\u2666 Arithm\u00e9tique : nombres premiers entre eux, parit\u00e9, divisibilit\u00e9 etc.<br \/>\n\u2666 Calcul num\u00e9rique : irrationalit\u00e9 de \u221a2 ; carr\u00e9s parfaits ; racine carr\u00e9e d&rsquo;un nombre positif<br \/>\n\u2666 Algorithmique : cr\u00e9ation d&rsquo;un programme avec boucles et conditions d&rsquo;arr\u00eats qui g\u00e9n\u00e8re des triplets irr\u00e9ductibles\n\t\t\t<a href=\"https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2022\/03\/Les-triangles-rectangles-entiers.pdf\" target=\"_blank\" rel=\"noopener\">\n\t\t\t\t\t\t\tT\u00e9l\u00e9charcher le document complet\n\t\t\t<\/a>\n\n","protected":false},"excerpt":{"rendered":"<p>Quels triangles rectangles ont des c\u00f4t\u00e9s de longueurs enti\u00e8res\u202f?<\/p>\n","protected":false},"author":3,"featured_media":2858,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[107],"tags":[],"niveau":[113,114],"type_situation":[116],"theme_maths":[120,121,118],"probleme_associe":[139],"type-expe":[],"class_list":{"0":"post-2855","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-situation-probleme","8":"niveau-cycle-4","9":"niveau-lycee","10":"type_situation-situation-probleme","11":"theme_maths-espace-et-geometrie","12":"theme_maths-grandeurs-et-mesures","13":"theme_maths-nombres-et-calculs","14":"probleme_associe-les-triangles-rectangles-entiers","15":"czr-hentry"},"rttpg_featured_image_url":{"full":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/TRIANGLESRECTANGLESENTIERS.png",377,142,false],"landscape":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/TRIANGLESRECTANGLESENTIERS.png",377,142,false],"portraits":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/TRIANGLESRECTANGLESENTIERS.png",377,142,false],"thumbnail":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/TRIANGLESRECTANGLESENTIERS-150x142.png",150,142,true],"medium":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/TRIANGLESRECTANGLESENTIERS-300x113.png",300,113,true],"large":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/TRIANGLESRECTANGLESENTIERS.png",377,142,false],"1536x1536":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/TRIANGLESRECTANGLESENTIERS.png",377,142,false],"2048x2048":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/TRIANGLESRECTANGLESENTIERS.png",377,142,false],"tc-grid-full":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/TRIANGLESRECTANGLESENTIERS.png",377,142,false],"tc-grid":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/TRIANGLESRECTANGLESENTIERS.png",377,142,false],"tc-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/TRIANGLESRECTANGLESENTIERS-270x142.png",270,142,true],"slider-full":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/TRIANGLESRECTANGLESENTIERS.png",377,142,false],"slider":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/TRIANGLESRECTANGLESENTIERS.png",377,142,false],"tc-sq-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/TRIANGLESRECTANGLESENTIERS.png",377,142,false],"tc-ws-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/TRIANGLESRECTANGLESENTIERS.png",377,142,false],"tc-ws-small-thumb":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/TRIANGLESRECTANGLESENTIERS.png",377,142,false],"tc-slider-small":["https:\/\/math.univ-lyon1.fr\/dream\/wp-content\/uploads\/2023\/12\/TRIANGLESRECTANGLESENTIERS.png",377,142,false]},"rttpg_author":{"display_name":"St\u00e9phanie CROQUELOIS","author_link":"https:\/\/math.univ-lyon1.fr\/dream\/?author=3"},"rttpg_comment":0,"rttpg_category":"<a href=\"https:\/\/math.univ-lyon1.fr\/dream\/?cat=107\" rel=\"category\">Situation Probl\u00e8me<\/a>","rttpg_excerpt":"Quels triangles rectangles ont des c\u00f4t\u00e9s de longueurs enti\u00e8res\u202f?","_links":{"self":[{"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/posts\/2855","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2855"}],"version-history":[{"count":10,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/posts\/2855\/revisions"}],"predecessor-version":[{"id":3827,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/posts\/2855\/revisions\/3827"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=\/wp\/v2\/media\/2858"}],"wp:attachment":[{"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2855"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2855"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2855"},{"taxonomy":"niveau","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Fniveau&post=2855"},{"taxonomy":"type_situation","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Ftype_situation&post=2855"},{"taxonomy":"theme_maths","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Ftheme_maths&post=2855"},{"taxonomy":"probleme_associe","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Fprobleme_associe&post=2855"},{"taxonomy":"type-expe","embeddable":true,"href":"https:\/\/math.univ-lyon1.fr\/dream\/index.php?rest_route=%2Fwp%2Fv2%2Ftype-expe&post=2855"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}